The invention relates to a device for generating polarization-entangled photons by means of parametric down-conversion, comprising a waveguide structure formed in a substrate of an optically non-linear material with periodically poled regions, wherein, when in operation, pump photons can be supplied from a pump laser to the waveguide structure, and wherein a separating means for separating the entangled photons for the separate further conduction of signal photons and idler photons, respectively, is arranged to follow the waveguide structure.
1. Field of the Invention
Devices for generating polarization-entangled photons are particularly used in quantum-cryptographic devices when generating a quantum key. In detail, quantum cryptography designates the technique of creating and distributing symmetric secrets, wherein the security—being a measure for the confidentiality and the unadulteratedness of two identical bit sequences generated at two spaced-apart locations—can be mathematically exactly proven with methods of quantum information theory (information-theoretical security). The generated and distributed symmetric secrets can later on be used, e.g., as a key for symmetric cryptographic encryption methods. In contrast, there exists no such proof of the security of conventional key distribution systems that are based on asymmetric cryptography.
2. Description of Related Art
Quantum cryptography has been developed interdisciplinarily between the scientific fields of quantum physics, quantum optics, information theory, cryptography and information technology. A survey of the basics and methods as well as the historical development of quantum cryptography is contained in the articles by Gisin, N., G. Ribordy, W. Tittel, H. Zbinden, “Quantum Cryptography”, 2002 Rev. Mod. Phys. 74, 145; and by Du{hacek over (s)}ek, M., N. Lütkenhaus, M. Hendrych, “Quantum Cryptography”, 2006, Progress in Optics, vol. 49, Edt. E. Wolf (Elsevier, 2006).
A conventional quantum-cryptographic link always comprises two stations, or apparatuses, respectively. In the literature, these stations commonly are termed ALICE and BOB components. These two stations set up at spaced-apart locations are connected by an optical quantum channel (fiberglass-bound or through free space) as well as by a conventional, classical, unencrypted, electronic communication channel, also termed public channel.
In its ALICE and BOB components, such a quantum-cryptographic connection continuously generates symmetric secrets (i.e. secrets identical in the ALICE and BOB components) which are delivered to the outside via data channels for further use, e.g. as a key in connected cryptographic systems.
In detail, in quantum cryptography, photons are exchanged between two partners, which photons contain quantum information. The two partners measure certain properties of these photons, such as, e.g., the plane of polarisation, obtain the same measurement results and, thus, are able of setting up an identical quantum key. Parts of the measurement results, such as, e.g., the exact points of time, are exchanged via public channels. In this manner, the two partners are able to exactly associate the individual measurements to each other.
In principle, there are two methods, i.e. the one using single photons and the one using entangled photons. In case of the single photon method, a partner generates a sequence of individual photons which are sent through a polarizer whose plane of polarization is randomly varied. The setting of the polarizer is transmitted to the other partner. If a photon is then registered by this other partner, its plane of polarization, too, will be unambiguously determined. With this method, however, it must be ensured that in fact always only one single photon is generated since if several photons of the same polarization are generated, a photon could be intercepted by a third party.
In the method of polarization-entangled photons, by a special technique two photons are simultaneously generated which contain the same quantum information. One photon each is sent to one of the two partners so that the two partners will simultaneously obtain an identical measurement result and, thus, each one of them can build the same quantum key for him/herself.
The basis of each device for generating entangled photons is the parametric down-conversion in a non-linear crystal in which pump photons (index p) are converted into so-called signal photons (index s) and idler photons (index i). Quantum-mechanically, the state |p is converted into the product state |si. What is responsible for this down-conversion process is the susceptibility sensor , which links the (square) non-linear polarization with the electric field E as follows:
            P      i              (        2        )              ⁡          (      t      )        =            ∑              j        ,        k                                  ⁢                  ⁢                  χ        ijk                  (          2          )                    ⁢                        E          j                ⁡                  (          t          )                    ⁢                        E          k                ⁡                  (          t          )                    
For the temporal Fourier components of the fields, the following correlation will result:
            P      i              (        2        )              ⁡          (                        ω          3                =                              ω            1                    +                      ω            2                              )        =            ∑              j        ,        k                                  ⁢                            d          ijk                ⁡                  (                                    -                              ω                3                                      ,                          ω              1                        ,                          ω              2                                )                    ⁢                        E          j                ⁡                  (                      ω            1                    )                    ⁢                        E          k                ⁡                  (                      ω            2                    )                    wherein the relationship χijk(2)=2dijk applies. When converting a pump photon into a signal photon and an idler photon, the conservation of the energy ωp=ωs+ωi as well as the phase matching condition βx,p=βx,s+βx,i must be satisfied, wherein ω is the angular frequency and βx= nω/c denotes the respective propagation constants. A wave propagation in x-direction has been assumed. n is the (effective) refraction index for the respective frequency/polarization of the electromagnetic wave, and c is the velocity of light in vacuum.
Since the phase matching condition Equation 1 cannot be met easily, it is suitable to use periodically poled crystals in which the ferro-electric domains having a poling period Λ are alternatingly poled in the (+c) and (−c) direction of the crystal. Thus, during the down-conversion process, the quasi-phase matching condition
                              β                      x            ,            p                          =                              β                          x              ,              s                                +                      β                          x              ,              i                                +                      m            ⁢                                          2                ⁢                π                            Λ                                                          (        2        )            must be met, wherein in this case, coupling between the pump, signal and idler fields is effected via the mth Fourier component of the susceptibility tensor .
In a z-oriented lithium niobate (LiNbO3) crystal, the largest non-linear coefficient is the coefficient d33=χ333(2)/2 which is linked with the type I down-conversion of a vertically (i.e. z-) polarized pump photon in vertically polarized signal photons and idler photons (transition ωpV→ωsV+ωiV). The non-linear coefficient which is responsible for the type I down conversion of a vertically polarized pump photon in horizontally polarized signal and idler photons (transition ωpV→ωsH+ωiH) is the coefficient d31=χ311(2)/2, the magnitude of which is only approximately one seventh of the magnitude of d33.
Assuming a negligible exhaustion of the pump wave (i.e. the output of the pump wave Pp remains approximately constant) and an ideal quasi-phase matching Equation 2, the efficiency η of the down-conversion when passing a path having the length L can be expressed as
                    η        =                                                            N                i                            ⁡                              (                L                )                                                                    N                s                            ⁡                              (                0                )                                              =                                    v              2                        ⁢                          κ              i              2                        ⁢                          L              2                        ⁢                          P              p                        ⁢                                                            ω                  s                                                  ω                  i                                            .                                                          (        3        )            Therein, Ni(L) and Ns(0), respectively, are the idler photon number at the output, and the signal photon number at the input; ν is the field overlap factor which describes the extent of the transversal overlapping of the pump fields, signal fields and idler fields, and κ is the coupling factor. It has been assumed that the idler photon number at the input is zero. The photon number is linked to the electromagnetic output of the wave via the relationship N=P/ηω. The coupling factor κi is calculated as
            κ      i        =                            ω          i                ⁢                  d          eff                                      2          ⁢                                          ⁢                      ɛ            0                    ⁢                      c            3                    ⁢                                    n              _                        p                    ⁢                                    n              _                        s                    ⁢                                    n              _                        i                                ,wherein deff is the mth Fourier component of the d-coefficient that is responsible for the down-conversion, and np, ns, ni are the (effective) refraction indexes for the pump, signal and idler waves; ∈0 is the dielectric constant of the vacuum.
The use of waveguides in non-linear optical components has the advantages of a pronounced local delimitation of the pump, signal and idler fields (increasing the field overlap factor ν), a great interaction length and the possibility of an efficient electrooptical tuning. Such waveguide designs per se are prior art in non-linear optical devices, such as frequency mixers (cf. e.g. R. V. Roussev, C. Langrock, J. R. Kurz, M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for the efficient single-photon detection at communication wavelengths”, Optics Letters, vol. 29, p. 1518 ff. (2004)), parametric oscillators (cf. e.g., X. Xie, M. M. Fejer, “Two-spatial-mode parametric amplifier in lithium niobate waveguides with asymmetric Y junctions”, Optics Letters, vol. 31, p. 799 ff (2006)), and also sources for entangled photons (S. Tanzilli, W. Tittel, H. De Riematten, H. Zbinden, P. Baldi, M. De Micheli, “PPLN waveguide for quantum communication”, Eur. Phys. J. D, vol. 18, p. 155 ff (2002).
So far, a number of different approaches have been used for generating polarization-entangled photons which quantum-mechanically correspond to a state of superposition
                                        Ψ          〉                =                              1                          2                                ⁢                      (                                                                                                  s                    H                                    〉                                ⁢                                                                        i                    H                                    〉                                            +                                                                  A                                                  ⁢                                  ⅇ                                      ⅈ                    ⁢                                                                                  ⁢                    φ                                                  ⁢                                                                        s                    V                                    〉                                ⁢                                                                        i                    V                                    〉                                                      )                                              (        4        )            with a phase shift φ between the horizontal and vertical states. Ideally, the constant |A| should have the value one.
As shown in the article by C. Kurtsiefer, M. Oberpaierleiter and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence”, Phys. Rev. A, vol. 64, p. 023802 ff (2001), one possible way of generating polarization-entangled photons is the use of type-II down-conversion. The disadvantage of this method is the necessity of optical devices for compensating the temperature drift, whereby a compact set-up (such as, e.g., on a single optical chip) is not possible.
The realization of two-crystal configurations, wherein the generation of horizontally and vertically polarized photons occurs by means of type-I conversion in two consecutively arranged non-linear crystals rotated relative to each other by 90 degrees, has been described in the articles P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, P. H. Eberhard, “Ultra-bright source of polarization-entangled photons”, Physical Review A, vol. 60, 773-776 (1999), and J. B. Altepeter, E. R. Jeffrey, P. G. Kwiat, “Phase-compensated ultra-bright source of entangled photons”, Optics Express, vol. 13, p. 8951 ff, 2005. Furthermore, two-crystal configurations have been suggested in which periodically poled LiNbO3 crystals were optically connected by means of fiberglass cables; cf. Y. K. Jiang, A. Tomita, “The generation of polarization-entangled photon pairs using periodically poled lithium niobate waveguides in a fibre loop”, J. Phys. B, vol. 40, p. 437 ff. (2007).
In the publication Y. K. Jiang, A. Tomita, “Highly efficient polarization-entangled photon source using periodically poled lithium niobate waveguides”, Optics Commun. vol. 267, p. 278 ff (2006), a source of photons is described which requires only one non-linear crystal. On the crystal, there are two spaced-apart wave-guides, vertically polarized photons being generated in each of them. For generating the horizontal polarization, one of these waveguides is followed by an external, fiber-coupled device for rotating the polarization.
For an efficient generation of photons with both polarizations, TM (vertically polarized) and TE (horizontally polarized), on one wafer, waveguides are required which support both TM modes and TE modes. Even though the SPE method (SPE—soft proton exchange) already addressed in the previous article by S. Tanzilli et al. (2002) is attractive with a view to obtaining PPLN waveguides (PPLN—periodically poled lithium niobate) with low losses, there do exist problems, since the proton exchange process only increases the extraordinary refraction index ne, yet leaves the ordinary refraction index no practically unchanged. Accordingly, when using this very well established technique, only waveguides that conduct TM modes can be obtained. As a remedy, titanium(Ti)- or zinc(Zn)-diffused or -doped waveguides have been provided which are capable of conducting both polarizations. Zn-doped waveguides are preferable, since Ti-diffused waveguides have the disadvantage of an increased susceptibility for optically induced damage.